There's only two Z80 TI-calcs which can convert HEX/DEC/OCT: the TI-85 and the TI-86; the 68k calcs are all capable of converting number systems as well: TI-92, TI-92+, TI-89, TI-89 Titanium, Voyage 200.
Apart from the 68k calcs and the Nspire calcs (ARM chips), all others use a Z80. The Nspire (without the CAS) emulate a TI-84, so does Z80 emulation.
The TI-84 Plus CE-T features an eZ80, which has a normal Z80 mode and an enhanced eZ80 mode that expands the registers to 24 bit and can multiply 8 bit registers in hardware. The clock cycles have also been optimised, so it's faster than a Z80 at the same speed.
All of the TI calcs allow assembly programming, the very early ones with loop holes only (TI-80, 81, 82, 85).
Some calcs allow for calculator apps (basically 16k programmes though multiple 16k apps can be used for one single program); those are all the 68k ones and the 83+ series and 84 series. The app needed to be signed by Texas Instruments, i.e. had to undergo a verification process, but some guys brute forced the private keys, and now everybody can do so.
This led Texas Instruments to produce the Nspire series which was deemed secure but had been cracked. The latest models (TI Nspire CX (CAS), and TI-84 Plus CE-T) seem to have a hardware protection to prevent unwanted changes. At least the 84 plus CE-T can be programmed in Z80 and eZ80, but you can't flash anything, AFAIK.
They are all best programmed via a PC as typing larger programms via the calcs keys is extremely awkward.
TI-BASIC is quite limited, IMO. And yes, the various versions differ.